LMFDB - Embedded newform 135.4.e.c.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(46,135)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("135.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{13} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$2.13089 + 3.69081i$ of defining polynomial
Character	$\chi$	$=$	135.46
Dual form			135.4.e.c.91.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13089 + 3.69081i) q^{2} +(-5.08138 - 8.80120i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-15.3820 + 26.6423i) q^{7} +9.21718 q^{8} +O(q^{10})$	\(q+(-2.13089 + 3.69081i) q^{2} +(-5.08138 - 8.80120i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-15.3820 + 26.6423i) q^{7} +9.21718 q^{8} +21.3089 q^{10} +(20.3573 - 35.2599i) q^{11} +(-31.6089 - 54.7482i) q^{13} +(-65.5545 - 113.544i) q^{14} +(21.0102 - 36.3908i) q^{16} +6.58990 q^{17} +75.3803 q^{19} +(-25.4069 + 44.0060i) q^{20} +(86.7584 + 150.270i) q^{22} +(-31.1814 - 54.0077i) q^{23} +(-12.5000 + 21.6506i) q^{25} +269.420 q^{26} +312.646 q^{28} +(24.8042 - 42.9621i) q^{29} +(-51.5021 - 89.2043i) q^{31} +(126.410 + 218.948i) q^{32} +(-14.0423 + 24.3221i) q^{34} +153.820 q^{35} -282.029 q^{37} +(-160.627 + 278.214i) q^{38} +(-23.0430 - 39.9116i) q^{40} +(-78.7700 - 136.434i) q^{41} +(168.907 - 292.555i) q^{43} -413.773 q^{44} +265.776 q^{46} +(22.2579 - 38.5518i) q^{47} +(-301.710 - 522.577i) q^{49} +(-53.2722 - 92.2702i) q^{50} +(-321.234 + 556.393i) q^{52} -26.2752 q^{53} -203.573 q^{55} +(-141.778 + 245.567i) q^{56} +(105.710 + 183.095i) q^{58} +(-212.963 - 368.863i) q^{59} +(-425.297 + 736.637i) q^{61} +438.981 q^{62} -741.296 q^{64} +(-158.045 + 273.741i) q^{65} +(-48.1538 - 83.4048i) q^{67} +(-33.4858 - 57.9990i) q^{68} +(-327.773 + 567.719i) q^{70} -952.164 q^{71} -50.8558 q^{73} +(600.973 - 1040.92i) q^{74} +(-383.036 - 663.437i) q^{76} +(626.271 + 1084.73i) q^{77} +(98.6395 - 170.849i) q^{79} -210.102 q^{80} +671.400 q^{82} +(-98.8693 + 171.247i) q^{83} +(-16.4747 - 28.5351i) q^{85} +(719.844 + 1246.81i) q^{86} +(187.637 - 324.997i) q^{88} -1364.54 q^{89} +1944.83 q^{91} +(-316.889 + 548.868i) q^{92} +(94.8583 + 164.299i) q^{94} +(-188.451 - 326.406i) q^{95} +(715.579 - 1239.42i) q^{97} +2571.64 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8	$ 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8} + 20 q^{10} - 23 q^{11} - 96 q^{13} + 21 q^{14} - 324 q^{16} + 322 q^{17} + 558 q^{19} - 180 q^{20} - 311 q^{22} - 96 q^{23} - 175 q^{25} - 716 q^{26} + 674 q^{28} + 296 q^{29} - 244 q^{31} + 314 q^{32} - 125 q^{34} + 220 q^{35} + 808 q^{37} - 305 q^{38} - 90 q^{40} + 47 q^{41} - 525 q^{43} + 110 q^{44} + 1434 q^{46} - 164 q^{47} - 1225 q^{49} - 50 q^{50} - 1682 q^{52} + 1012 q^{53} + 230 q^{55} + 981 q^{56} - 1183 q^{58} + 85 q^{59} - 828 q^{61} - 1572 q^{62} + 4472 q^{64} - 480 q^{65} - 1093 q^{67} - 2473 q^{68} + 105 q^{70} + 656 q^{71} + 4170 q^{73} + 1316 q^{74} - 2789 q^{76} - 24 q^{77} - 2110 q^{79} + 3240 q^{80} - 124 q^{82} - 1290 q^{83} - 805 q^{85} + 2569 q^{86} - 2271 q^{88} - 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 517 q^{94} - 1395 q^{95} - 1787 q^{97} + 2558 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8 + 20 * q^10 - 23 * q^11 - 96 * q^13 + 21 * q^14 - 324 * q^16 + 322 * q^17 + 558 * q^19 - 180 * q^20 - 311 * q^22 - 96 * q^23 - 175 * q^25 - 716 * q^26 + 674 * q^28 + 296 * q^29 - 244 * q^31 + 314 * q^32 - 125 * q^34 + 220 * q^35 + 808 * q^37 - 305 * q^38 - 90 * q^40 + 47 * q^41 - 525 * q^43 + 110 * q^44 + 1434 * q^46 - 164 * q^47 - 1225 * q^49 - 50 * q^50 - 1682 * q^52 + 1012 * q^53 + 230 * q^55 + 981 * q^56 - 1183 * q^58 + 85 * q^59 - 828 * q^61 - 1572 * q^62 + 4472 * q^64 - 480 * q^65 - 1093 * q^67 - 2473 * q^68 + 105 * q^70 + 656 * q^71 + 4170 * q^73 + 1316 * q^74 - 2789 * q^76 - 24 * q^77 - 2110 * q^79 + 3240 * q^80 - 124 * q^82 - 1290 * q^83 - 805 * q^85 + 2569 * q^86 - 2271 * q^88 - 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 517 * q^94 - 1395 * q^95 - 1787 * q^97 + 2558 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.13089	+	3.69081i	−0.753383	+	1.30490i	0.192791	+	0.981240i	$0.438246\pi$
$2$	−2.13089	+	3.69081i	−0.753383	+	1.30490i	−0.946174	+	0.323658i	$0.895087\pi$
$3$		0			0
$3$		0			0
$4$	−5.08138	−	8.80120i	−0.635172	−	1.10015i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	−15.3820	+	26.6423i	−0.830548	+	1.43855i	0.0670561	+	0.997749i	$0.478639\pi$
$7$	−15.3820	+	26.6423i	−0.830548	+	1.43855i	−0.897604	+	0.440802i	$0.854694\pi$
$8$	9.21718			0.407346
$9$		0			0
$10$	21.3089			0.673846
$11$	20.3573	−	35.2599i	0.557996	−	0.966478i	−0.439667	−	0.898161i	$-0.644904\pi$
$11$	20.3573	−	35.2599i	0.557996	−	0.966478i	0.997664	−	0.0683175i	$-0.0217631\pi$
$12$		0			0
$13$	−31.6089	−	54.7482i	−0.674364	−	1.16803i	−0.976654	−	0.214817i	$-0.931085\pi$
$13$	−31.6089	−	54.7482i	−0.674364	−	1.16803i	0.302290	−	0.953216i	$-0.402249\pi$
$14$	−65.5545	−	113.544i	−1.25144	−	2.16756i
$15$		0			0
$16$	21.0102	−	36.3908i	0.328285	−	0.568606i
$17$	6.58990			0.0940168			0.0470084	−	0.998894i	$-0.485031\pi$
$17$	6.58990			0.0940168			0.0470084	+	0.998894i	$0.485031\pi$
$18$		0			0
$19$	75.3803			0.910180			0.455090	−	0.890445i	$-0.349607\pi$
$19$	75.3803			0.910180			0.455090	+	0.890445i	$0.349607\pi$
$20$	−25.4069	+	44.0060i	−0.284058	+	0.492002i
$21$		0			0
$22$	86.7584	+	150.270i	0.840770	+	1.45626i
$23$	−31.1814	−	54.0077i	−0.282686	−	0.489626i	0.689360	−	0.724419i	$-0.257892\pi$
$23$	−31.1814	−	54.0077i	−0.282686	−	0.489626i	−0.972045	+	0.234793i	$0.924559\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	269.420			2.03222
$27$		0			0
$28$	312.646			2.11016
$29$	24.8042	−	42.9621i	0.158828	−	0.275099i	−0.775618	−	0.631202i	$-0.782562\pi$
$29$	24.8042	−	42.9621i	0.158828	−	0.275099i	0.934446	+	0.356104i	$0.115895\pi$
$30$		0			0
$31$	−51.5021	−	89.2043i	−0.298389	−	0.516824i	0.677379	−	0.735634i	$-0.263116\pi$
$31$	−51.5021	−	89.2043i	−0.298389	−	0.516824i	−0.975767	+	0.218810i	$0.929783\pi$
$32$	126.410	+	218.948i	0.698321	+	1.20953i
$33$		0			0
$34$	−14.0423	+	24.3221i	−0.0708306	+	0.122682i
$35$	153.820			0.742865
$36$		0			0
$37$	−282.029			−1.25312			−0.626559	−	0.779374i	$-0.715537\pi$
$37$	−282.029			−1.25312			−0.626559	+	0.779374i	$0.715537\pi$
$38$	−160.627	+	278.214i	−0.685714	+	1.18769i
$39$		0			0
$40$	−23.0430	−	39.9116i	−0.0910853	−	0.157764i
$41$	−78.7700	−	136.434i	−0.300044	−	0.519692i	0.676102	−	0.736808i	$-0.263668\pi$
$41$	−78.7700	−	136.434i	−0.300044	−	0.519692i	−0.976146	+	0.217117i	$0.930335\pi$
$42$		0			0
$43$	168.907	−	292.555i	0.599025	−	1.03754i	−0.393940	−	0.919136i	$-0.628888\pi$
$43$	168.907	−	292.555i	0.599025	−	1.03754i	0.992965	−	0.118406i	$-0.0377783\pi$
$44$	−413.773			−1.41770
$45$		0			0
$46$	265.776			0.851882
$47$	22.2579	−	38.5518i	0.0690777	−	0.119646i	−0.829418	−	0.558629i	$-0.811328\pi$
$47$	22.2579	−	38.5518i	0.0690777	−	0.119646i	0.898496	+	0.438983i	$0.144661\pi$
$48$		0			0
$49$	−301.710	−	522.577i	−0.879620	−	1.52355i
$50$	−53.2722	−	92.2702i	−0.150677	−	0.260980i
$51$		0			0
$52$	−321.234	+	556.393i	−0.856675	+	1.48380i
$53$	−26.2752			−0.0680978			−0.0340489	−	0.999420i	$-0.510840\pi$
$53$	−26.2752			−0.0680978			−0.0340489	+	0.999420i	$0.510840\pi$
$54$		0			0
$55$	−203.573			−0.499087
$56$	−141.778	+	245.567i	−0.338320	+	0.585988i
$57$		0			0
$58$	105.710	+	183.095i	0.239317	+	0.414509i
$59$	−212.963	−	368.863i	−0.469923	−	0.813930i	0.529486	−	0.848319i	$-0.322385\pi$
$59$	−212.963	−	368.863i	−0.469923	−	0.813930i	−0.999409	+	0.0343889i	$0.989052\pi$
$60$		0			0
$61$	−425.297	+	736.637i	−0.892684	+	1.54617i	−0.0560400	+	0.998429i	$0.517847\pi$
$61$	−425.297	+	736.637i	−0.892684	+	1.54617i	−0.836644	+	0.547746i	$0.815486\pi$
$62$	438.981			0.899204
$63$		0			0
$64$	−741.296			−1.44784
$65$	−158.045	+	273.741i	−0.301585	+	0.522360i
$66$		0			0
$67$	−48.1538	−	83.4048i	−0.0878048	−	0.152082i	0.818778	−	0.574110i	$-0.194652\pi$
$67$	−48.1538	−	83.4048i	−0.0878048	−	0.152082i	−0.906583	+	0.422028i	$0.861319\pi$
$68$	−33.4858	−	57.9990i	−0.0597168	−	0.103433i
$69$		0			0
$70$	−327.773	+	567.719i	−0.559662	+	0.969363i
$71$	−952.164			−1.59156			−0.795782	−	0.605583i	$-0.792940\pi$
$71$	−952.164			−1.59156			−0.795782	+	0.605583i	$0.792940\pi$
$72$		0			0
$73$	−50.8558			−0.0815373			−0.0407686	−	0.999169i	$-0.512981\pi$
$73$	−50.8558			−0.0815373			−0.0407686	+	0.999169i	$0.512981\pi$
$74$	600.973	−	1040.92i	0.944077	−	1.63519i
$75$		0			0
$76$	−383.036	−	663.437i	−0.578121	−	1.00134i
$77$	626.271	+	1084.73i	0.926886	+	1.60541i
$78$		0			0
$79$	98.6395	−	170.849i	0.140479	−	0.243316i	−0.787198	−	0.616700i	$-0.788469\pi$
$79$	98.6395	−	170.849i	0.140479	−	0.243316i	0.927677	+	0.373384i	$0.121803\pi$
$80$	−210.102			−0.293627
$81$		0			0
$82$	671.400			0.904192
$83$	−98.8693	+	171.247i	−0.130751	+	0.226467i	−0.923966	−	0.382474i	$-0.875072\pi$
$83$	−98.8693	+	171.247i	−0.130751	+	0.226467i	0.793215	+	0.608941i	$0.208405\pi$
$84$		0			0
$85$	−16.4747	−	28.5351i	−0.0210228	−	0.0364125i
$86$	719.844	+	1246.81i	0.902590	+	1.56333i
$87$		0			0
$88$	187.637	−	324.997i	0.227298	−	0.393691i
$89$	−1364.54			−1.62519			−0.812593	−	0.582832i	$-0.801944\pi$
$89$	−1364.54			−1.62519			−0.812593	+	0.582832i	$0.801944\pi$
$90$		0			0
$91$	1944.83			2.24037
$92$	−316.889	+	548.868i	−0.359108	+	0.621993i
$93$		0			0
$94$	94.8583	+	164.299i	0.104084	+	0.180279i
$95$	−188.451	−	326.406i	−0.203522	−	0.352511i
$96$		0			0
$97$	715.579	−	1239.42i	0.749031	−	1.29736i	−0.199256	−	0.979947i	$-0.563853\pi$
$97$	715.579	−	1239.42i	0.749031	−	1.29736i	0.948288	−	0.317413i	$-0.102814\pi$
$98$	2571.64			2.65076
$99$		0			0
$100$	254.069			0.254069
$101$	553.808	−	959.224i	0.545604	−	0.945013i	−0.452965	−	0.891528i	$-0.649634\pi$
$101$	553.808	−	959.224i	0.545604	−	0.945013i	0.998569	−	0.0534851i	$-0.0170329\pi$
$102$		0			0
$103$	−264.437	−	458.018i	−0.252969	−	0.438154i	0.711373	−	0.702814i	$-0.248074\pi$
$103$	−264.437	−	458.018i	−0.252969	−	0.438154i	−0.964342	+	0.264660i	$0.914740\pi$
$104$	−291.345	−	504.624i	−0.274699	−	0.475793i
$105$		0			0
$106$	55.9896	−	96.9769i	0.0513037	−	0.0888607i
$107$	−490.910			−0.443533			−0.221766	−	0.975100i	$-0.571182\pi$
$107$	−490.910			−0.443533			−0.221766	+	0.975100i	$0.571182\pi$
$108$		0			0
$109$	−351.634			−0.308994			−0.154497	−	0.987993i	$-0.549376\pi$
$109$	−351.634			−0.308994			−0.154497	+	0.987993i	$0.549376\pi$
$110$	433.792	−	751.349i	0.376004	−	0.651258i
$111$		0			0
$112$	646.357	+	1119.52i	0.545313	+	0.944509i
$113$	881.226	+	1526.33i	0.733618	+	1.27066i	0.955327	+	0.295550i	$0.0955030\pi$
$113$	881.226	+	1526.33i	0.733618	+	1.27066i	−0.221710	+	0.975113i	$0.571164\pi$
$114$		0			0
$115$	−155.907	+	270.039i	−0.126421	+	0.218967i
$116$	−504.158			−0.403533
$117$		0			0
$118$	1815.20			1.41613
$119$	−101.366	+	175.570i	−0.0780854	+	0.135248i
$120$		0			0
$121$	−163.340	−	282.914i	−0.122720	−	0.212557i
$122$	−1812.52	−	3139.38i	−1.34507	−	2.32972i
$123$		0			0
$124$	−523.403	+	906.561i	−0.379056	+	0.656545i
$125$	125.000			0.0894427
$126$		0			0
$127$	−1506.12			−1.05234			−0.526169	−	0.850380i	$-0.676372\pi$
$127$	−1506.12			−1.05234			−0.526169	+	0.850380i	$0.676372\pi$
$128$	568.343	−	984.399i	0.392460	−	0.679761i
$129$		0			0
$130$	−673.551	−	1166.62i	−0.454418	−	0.787075i
$131$	637.562	+	1104.29i	0.425222	+	0.736506i	0.996441	−	0.0842915i	$-0.0268627\pi$
$131$	637.562	+	1104.29i	0.425222	+	0.736506i	−0.571219	+	0.820798i	$0.693529\pi$
$132$		0			0
$133$	−1159.50	+	2008.31i	−0.755948	+	1.30934i
$134$	410.441			0.264603
$135$		0			0
$136$	60.7403			0.0382973
$137$	719.712	−	1246.58i	0.448826	−	0.777389i	−0.549484	−	0.835504i	$-0.685176\pi$
$137$	719.712	−	1246.58i	0.448826	−	0.777389i	0.998310	+	0.0581150i	$0.0185090\pi$
$138$		0			0
$139$	1269.75	+	2199.27i	0.774811	+	1.34201i	0.934901	+	0.354909i	$0.115488\pi$
$139$	1269.75	+	2199.27i	0.774811	+	1.34201i	−0.160090	+	0.987102i	$0.551178\pi$
$140$	−781.616	−	1353.80i	−0.471847	−	0.817263i
$141$		0			0
$142$	2028.96	−	3514.25i	1.19906	−	2.07683i
$143$	−2573.89			−1.50517
$144$		0			0
$145$	−248.042			−0.142060
$146$	108.368	−	187.699i	0.0614288	−	0.106398i
$147$		0			0
$148$	1433.10	+	2482.20i	0.795945	+	1.37862i
$149$	46.8796	+	81.1979i	0.0257754	+	0.0446442i	0.878625	−	0.477512i	$-0.158461\pi$
$149$	46.8796	+	81.1979i	0.0257754	+	0.0446442i	−0.852850	+	0.522156i	$0.825128\pi$
$150$		0			0
$151$	534.065	−	925.027i	0.287825	−	0.498527i	−0.685465	−	0.728105i	$-0.740401\pi$
$151$	534.065	−	925.027i	0.287825	−	0.498527i	0.973290	+	0.229578i	$0.0737345\pi$
$152$	694.794			0.370758
$153$		0			0
$154$	−5338.06			−2.79320
$155$	−257.510	+	446.021i	−0.133443	+	0.231131i
$156$		0			0
$157$	−90.8574	−	157.370i	−0.0461861	−	0.0799966i	0.842008	−	0.539465i	$-0.181373\pi$
$157$	−90.8574	−	157.370i	−0.0461861	−	0.0799966i	−0.888194	+	0.459468i	$0.848040\pi$
$158$	420.380	+	728.119i	0.211668	+	0.366621i
$159$		0			0
$160$	632.048	−	1094.74i	0.312299	−	0.540917i
$161$	1918.52			0.939136
$162$		0			0
$163$	−1103.07			−0.530056			−0.265028	−	0.964241i	$-0.585381\pi$
$163$	−1103.07			−0.530056			−0.265028	+	0.964241i	$0.585381\pi$
$164$	−800.520	+	1386.54i	−0.381159	+	0.660187i
$165$		0			0
$166$	−421.359	−	729.816i	−0.197011	−	0.341233i
$167$	−2020.85	−	3500.22i	−0.936396	−	1.62189i	−0.772126	−	0.635470i	$-0.780806\pi$
$167$	−2020.85	−	3500.22i	−0.936396	−	1.62189i	−0.164270	−	0.986415i	$-0.552527\pi$
$168$		0			0
$169$	−899.745	+	1558.40i	−0.409534	+	0.709333i
$170$	140.423			0.0633529
$171$		0			0
$172$	−3433.12			−1.52194
$173$	−1373.88	+	2379.63i	−0.603780	+	1.04578i	0.388463	+	0.921465i	$0.373006\pi$
$173$	−1373.88	+	2379.63i	−0.603780	+	1.04578i	−0.992243	+	0.124314i	$0.960327\pi$
$174$		0			0
$175$	−384.549	−	666.059i	−0.166110	−	0.287710i
$176$	−855.423	−	1481.64i	−0.366363	−	0.634560i
$177$		0			0
$178$	2907.69	−	5036.27i	1.22439	−	2.12070i
$179$	2838.32			1.18517			0.592587	−	0.805506i	$-0.298107\pi$
$179$	2838.32			1.18517			0.592587	+	0.805506i	$0.298107\pi$
$180$		0			0
$181$	3442.25			1.41359			0.706796	−	0.707417i	$-0.250140\pi$
$181$	3442.25			1.41359			0.706796	+	0.707417i	$0.250140\pi$
$182$	−4144.21	+	7177.99i	−1.68785	+	2.92345i
$183$		0			0
$184$	−287.405	−	497.799i	−0.115151	−	0.199447i
$185$	705.073	+	1221.22i	0.280206	+	0.485330i
$186$		0			0
$187$	134.153	−	232.359i	0.0524610	−	0.0908652i
$188$	−452.403			−0.175505
$189$		0			0
$190$	1606.27			0.613322
$191$	−373.148	+	646.311i	−0.141361	+	0.244845i	−0.928010	−	0.372557i	$-0.878481\pi$
$191$	−373.148	+	646.311i	−0.141361	+	0.244845i	0.786648	+	0.617402i	$0.211815\pi$
$192$		0			0
$193$	−53.9538	−	93.4506i	−0.0201227	−	0.0348535i	0.855789	−	0.517326i	$-0.173072\pi$
$193$	−53.9538	−	93.4506i	−0.0201227	−	0.0348535i	−0.875911	+	0.482472i	$0.839739\pi$
$194$	3049.64	+	5282.13i	1.12861	+	1.95482i
$195$		0			0
$196$	−3066.20	+	5310.82i	−1.11742	+	1.93543i
$197$	3361.02			1.21555			0.607774	−	0.794110i	$-0.292063\pi$
$197$	3361.02			1.21555			0.607774	+	0.794110i	$0.292063\pi$
$198$		0			0
$199$	1368.99			0.487663			0.243831	−	0.969818i	$-0.421596\pi$
$199$	1368.99			0.487663			0.243831	+	0.969818i	$0.421596\pi$
$200$	−115.215	+	199.558i	−0.0407346	+	0.0705544i
$201$		0			0
$202$	2360.21	+	4088.00i	0.822097	+	1.42391i
$203$	763.074	+	1321.68i	0.263829	+	0.456965i
$204$		0			0
$205$	−393.850	+	682.168i	−0.134184	+	0.232413i
$206$	2253.94			0.762329
$207$		0			0
$208$	−2656.44			−0.885534
$209$	1534.54	−	2657.90i	0.507877	−	0.879669i
$210$		0			0
$211$	−1251.27	−	2167.27i	−0.408252	−	0.707114i	0.586442	−	0.809991i	$-0.300528\pi$
$211$	−1251.27	−	2167.27i	−0.408252	−	0.707114i	−0.994694	+	0.102878i	$0.967195\pi$
$212$	133.514	+	231.254i	0.0432538	+	0.0749178i
$213$		0			0
$214$	1046.07	−	1811.85i	0.334150	−	0.578765i
$215$	−1689.07			−0.535784
$216$		0			0
$217$	3168.81			0.991305
$218$	749.292	−	1297.81i	0.232791	−	0.403206i
$219$		0			0
$220$	1034.43	+	1791.69i	0.317006	+	0.549071i
$221$	−208.299	−	360.785i	−0.0634015	−	0.109815i
$222$		0			0
$223$	−937.263	+	1623.39i	−0.281452	+	0.487489i	−0.971743	−	0.236043i	$-0.924149\pi$
$223$	−937.263	+	1623.39i	−0.281452	+	0.487489i	0.690291	+	0.723532i	$0.257483\pi$
$224$	−7777.72			−2.31996
$225$		0			0
$226$	−7511.18			−2.21078
$227$	2539.37	−	4398.32i	0.742484	−	1.28602i	−0.208877	−	0.977942i	$-0.566981\pi$
$227$	2539.37	−	4398.32i	0.742484	−	1.28602i	0.951361	−	0.308078i	$-0.0996859\pi$
$228$		0			0
$229$	−432.933	−	749.861i	−0.124930	−	0.216385i	0.796776	−	0.604275i	$-0.206537\pi$
$229$	−432.933	−	749.861i	−0.124930	−	0.216385i	−0.921706	+	0.387890i	$0.873204\pi$
$230$	−664.441	−	1150.85i	−0.190487	−	0.329933i
$231$		0			0
$232$	228.625	−	395.990i	0.0646981	−	0.112060i
$233$	−1142.10			−0.321122			−0.160561	−	0.987026i	$-0.551330\pi$
$233$	−1142.10			−0.321122			−0.160561	+	0.987026i	$0.551330\pi$
$234$		0			0
$235$	−222.579			−0.0617849
$236$	−2164.29	+	3748.66i	−0.596964	+	1.03397i
$237$		0			0
$238$	−431.998	−	748.242i	−0.117657	−	0.203787i
$239$	−1574.68	−	2727.43i	−0.426183	−	0.738171i	0.570347	−	0.821404i	$-0.306809\pi$
$239$	−1574.68	−	2727.43i	−0.426183	−	0.738171i	−0.996530	+	0.0832330i	$0.973475\pi$
$240$		0			0
$241$	−2252.18	+	3900.90i	−0.601975	+	1.04265i	0.390547	+	0.920583i	$0.372286\pi$
$241$	−2252.18	+	3900.90i	−0.601975	+	1.04265i	−0.992522	+	0.122068i	$0.961047\pi$
$242$	1392.24			0.369821
$243$		0			0
$244$	8644.39			2.26803
$245$	−1508.55	+	2612.88i	−0.393378	+	0.681351i
$246$		0			0
$247$	−2382.69	−	4126.94i	−0.613793	−	1.06312i
$248$	−474.704	−	822.212i	−0.121547	−	0.210526i
$249$		0			0
$250$	−266.361	+	461.351i	−0.0673846	+	0.116714i
$251$	−886.861			−0.223021			−0.111510	−	0.993763i	$-0.535569\pi$
$251$	−886.861			−0.223021			−0.111510	+	0.993763i	$0.535569\pi$
$252$		0			0
$253$	−2539.08			−0.630950
$254$	3209.38	−	5558.81i	0.792813	−	1.37319i
$255$		0			0
$256$	−543.033	−	940.561i	−0.132576	−	0.229629i
$257$	1131.02	+	1958.98i	0.274517	+	0.475478i	0.970013	−	0.243052i	$-0.0781486\pi$
$257$	1131.02	+	1958.98i	0.274517	+	0.475478i	−0.695496	+	0.718530i	$0.744815\pi$
$258$		0			0
$259$	4338.17	−	7513.92i	1.04077	−	1.80267i
$260$	3212.34			0.766233
$261$		0			0
$262$	−5434.30			−1.28142
$263$	3640.31	−	6305.20i	0.853503	−	1.47831i	−0.0245245	−	0.999699i	$-0.507807\pi$
$263$	3640.31	−	6305.20i	0.853503	−	1.47831i	0.878027	−	0.478611i	$-0.158859\pi$
$264$		0			0
$265$	65.6881	+	113.775i	0.0152271	+	0.0263742i
$266$	−4941.52	−	8558.96i	−1.13904	−	1.97287i
$267$		0			0
$268$	−489.375	+	847.622i	−0.111542	+	0.193197i
$269$	106.781			0.0242028			0.0121014	−	0.999927i	$-0.496148\pi$
$269$	106.781			0.0242028			0.0121014	+	0.999927i	$0.496148\pi$
$270$		0			0
$271$	5908.85			1.32449			0.662246	−	0.749287i	$-0.269603\pi$
$271$	5908.85			1.32449			0.662246	+	0.749287i	$0.269603\pi$
$272$	138.455	−	239.811i	0.0308643	−	0.0534585i
$273$		0			0
$274$	3067.25	+	5312.64i	0.676276	+	1.17134i
$275$	508.933	+	881.498i	0.111599	+	0.193296i
$276$		0			0
$277$	−1645.04	+	2849.30i	−0.356827	+	0.618042i	−0.987429	−	0.158064i	$-0.949475\pi$
$277$	−1645.04	+	2849.30i	−0.356827	+	0.618042i	0.630602	+	0.776106i	$0.282808\pi$
$278$	−10822.8			−2.33492
$279$		0			0
$280$	1417.78			0.302603
$281$	169.861	−	294.209i	0.0360608	−	0.0624591i	−0.847432	−	0.530904i	$-0.821852\pi$
$281$	169.861	−	294.209i	0.0360608	−	0.0624591i	0.883493	+	0.468445i	$0.155186\pi$
$282$		0			0
$283$	−1299.83	−	2251.37i	−0.273028	−	0.472898i	0.696608	−	0.717452i	$-0.254692\pi$
$283$	−1299.83	−	2251.37i	−0.273028	−	0.472898i	−0.969636	+	0.244554i	$0.921358\pi$
$284$	4838.30	+	8380.19i	1.01092	+	1.75096i
$285$		0			0
$286$	5484.67	−	9499.73i	1.13397	−	1.96409i
$287$	4846.55			0.996804
$288$		0			0
$289$	−4869.57			−0.991161
$290$	528.550	−	915.475i	0.107026	−	0.185374i
$291$		0			0
$292$	258.418	+	447.592i	0.0517902	+	0.0897033i
$293$	89.0427	+	154.227i	0.0177540	+	0.0307509i	0.874766	−	0.484546i	$-0.161015\pi$
$293$	89.0427	+	154.227i	0.0177540	+	0.0307509i	−0.857012	+	0.515297i	$0.827682\pi$
$294$		0			0
$295$	−1064.82	+	1844.31i	−0.210156	+	0.364001i
$296$	−2599.52			−0.510452
$297$		0			0
$298$	−399.581			−0.0776749
$299$	−1971.22	+	3414.25i	−0.381266	+	0.660372i
$300$		0			0
$301$	5196.24	+	9000.16i	0.995038	+	1.72346i
$302$	2276.07	+	3942.26i	0.433685	+	0.751164i
$303$		0			0
$304$	1583.76	−	2743.15i	0.298798	−	0.517534i
$305$	4252.97			0.798441
$306$		0			0
$307$	1537.60			0.285848			0.142924	−	0.989734i	$-0.454349\pi$
$307$	1537.60			0.285848			0.142924	+	0.989734i	$0.454349\pi$
$308$	6364.64	−	11023.9i	1.17746	−	2.03943i
$309$		0			0
$310$	−1097.45	−	1900.84i	−0.201068	−	0.348260i
$311$	472.662	+	818.674i	0.0861807	+	0.149269i	0.905894	−	0.423505i	$-0.139200\pi$
$311$	472.662	+	818.674i	0.0861807	+	0.149269i	−0.819713	+	0.572774i	$0.805867\pi$
$312$		0			0
$313$	−992.767	+	1719.52i	−0.179280	+	0.310521i	−0.941634	−	0.336638i	$-0.890710\pi$
$313$	−992.767	+	1719.52i	−0.179280	+	0.310521i	0.762354	+	0.647160i	$0.224043\pi$
$314$	774.428			0.139183
$315$		0			0
$316$	−2004.90			−0.356913
$317$	−2591.62	+	4488.81i	−0.459179	+	0.795321i	−0.998918	−	0.0465112i	$-0.985190\pi$
$317$	−2591.62	+	4488.81i	−0.459179	+	0.795321i	0.539739	+	0.841833i	$0.318523\pi$
$318$		0			0
$319$	−1009.89	−	1749.19i	−0.177251	−	0.307008i
$320$	1853.24	+	3209.91i	0.323748	+	0.560748i
$321$		0			0
$322$	−4088.16	+	7080.91i	−0.707529	+	1.22548i
$323$	496.748			0.0855722
$324$		0			0
$325$	1580.45			0.269746
$326$	2350.52	−	4071.22i	0.399336	−	0.691670i
$327$		0			0
$328$	−726.037	−	1257.53i	−0.122222	−	0.211694i
$329$	684.741	+	1186.01i	0.114745	+	0.198744i
$330$		0			0
$331$	1086.68	−	1882.19i	0.180451	−	0.312551i	−0.761583	−	0.648067i	$-0.775578\pi$
$331$	1086.68	−	1882.19i	0.180451	−	0.312551i	0.942034	+	0.335517i	$0.108911\pi$
$332$	2009.57			0.332197
$333$		0			0
$334$	17224.8			2.82186
$335$	−240.769	+	417.024i	−0.0392675	+	0.0680133i
$336$		0			0
$337$	3925.16	+	6798.57i	0.634472	+	1.09894i	0.986627	+	0.162995i	$0.0521156\pi$
$337$	3925.16	+	6798.57i	0.634472	+	1.09894i	−0.352155	+	0.935942i	$0.614551\pi$
$338$	−3834.52	−	6641.58i	−0.617071	−	1.06880i
$339$		0			0
$340$	−167.429	+	289.995i	−0.0267062	+	0.0462565i
$341$	−4193.78			−0.665999
$342$		0			0
$343$	8011.53			1.26117
$344$	1556.85	−	2696.54i	0.244010	−	0.422638i
$345$		0			0
$346$	−5855.16	−	10141.4i	−0.909756	−	1.57574i
$347$	−4686.12	−	8116.60i	−0.724969	−	1.25568i	−0.958987	−	0.283451i	$-0.908521\pi$
$347$	−4686.12	−	8116.60i	−0.724969	−	1.25568i	0.234018	−	0.972232i	$-0.424813\pi$
$348$		0			0
$349$	588.952	−	1020.10i	0.0903321	−	0.156460i	−0.817319	−	0.576186i	$-0.804540\pi$
$349$	588.952	−	1020.10i	0.0903321	−	0.156460i	0.907651	+	0.419726i	$0.137874\pi$
$350$	3277.73			0.500577
$351$		0			0
$352$	10293.4			1.55864
$353$	−3631.06	+	6289.19i	−0.547484	+	0.948271i	0.450962	+	0.892543i	$0.351081\pi$
$353$	−3631.06	+	6289.19i	−0.547484	+	0.948271i	−0.998446	+	0.0557274i	$0.982252\pi$
$354$		0			0
$355$	2380.41	+	4122.99i	0.355885	+	0.616410i
$356$	6933.77	+	12009.6i	1.03227	+	1.78795i
$357$		0			0
$358$	−6048.15	+	10475.7i	−0.892890	+	1.54653i
$359$	1939.95			0.285199			0.142600	−	0.989780i	$-0.454454\pi$
$359$	1939.95			0.285199			0.142600	+	0.989780i	$0.454454\pi$
$360$		0			0
$361$	−1176.81			−0.171572
$362$	−7335.05	+	12704.7i	−1.06498	+	1.84459i
$363$		0			0
$364$	−9882.41	−	17116.8i	−1.42302	−	2.46474i
$365$	127.139	+	220.212i	0.0182323	+	0.0315792i
$366$		0			0
$367$	−3250.97	+	5630.85i	−0.462396	+	0.800893i	−0.999080	−	0.0428901i	$-0.986343\pi$
$367$	−3250.97	+	5630.85i	−0.462396	+	0.800893i	0.536684	+	0.843783i	$0.319677\pi$
$368$	−2620.51			−0.371205
$369$		0			0
$370$	−6009.73			−0.844409
$371$	404.165	−	700.034i	0.0565585	−	0.0979622i
$372$		0			0
$373$	−6659.02	−	11533.8i	−0.924372	−	1.60106i	−0.792568	−	0.609784i	$-0.791256\pi$
$373$	−6659.02	−	11533.8i	−0.924372	−	1.60106i	−0.131805	−	0.991276i	$-0.542077\pi$
$374$	571.729	+	990.263i	0.0790465	+	0.136913i
$375$		0			0
$376$	205.155	−	355.339i	0.0281385	−	0.0487373i
$377$	−3136.13			−0.428432
$378$		0			0
$379$	−3198.42			−0.433488			−0.216744	−	0.976228i	$-0.569544\pi$
$379$	−3198.42			−0.433488			−0.216744	+	0.976228i	$0.569544\pi$
$380$	−1915.18	+	3317.19i	−0.258544	+	0.447811i
$381$		0			0
$382$	−1590.27	−	2754.43i	−0.212999	−	0.368924i
$383$	−1170.25	−	2026.93i	−0.156128	−	0.270422i	0.777341	−	0.629079i	$-0.216568\pi$
$383$	−1170.25	−	2026.93i	−0.156128	−	0.270422i	−0.933469	+	0.358658i	$0.883235\pi$
$384$		0			0
$385$	3131.36	−	5423.67i	0.414516	−	0.717963i
$386$	459.878			0.0606403
$387$		0			0
$388$	−14544.5			−1.90305
$389$	1995.97	−	3457.12i	0.260153	−	0.450599i	−0.706129	−	0.708083i	$-0.749560\pi$
$389$	1995.97	−	3457.12i	0.260153	−	0.450599i	0.966282	+	0.257484i	$0.0828936\pi$
$390$		0			0
$391$	−205.482	−	355.906i	−0.0265772	−	0.0460330i
$392$	−2780.91	−	4816.69i	−0.358310	−	0.620611i
$393$		0			0
$394$	−7161.96	+	12404.9i	−0.915773	+	1.58616i
$395$	−986.395			−0.125648
$396$		0			0
$397$	−4960.90			−0.627155			−0.313577	−	0.949563i	$-0.601528\pi$
$397$	−4960.90			−0.627155			−0.313577	+	0.949563i	$0.601528\pi$
$398$	−2917.16	+	5052.66i	−0.367397	+	0.636350i
$399$		0			0
$400$	525.256	+	909.769i	0.0656569	+	0.113721i
$401$	413.811	+	716.742i	0.0515330	+	0.0892578i	0.890641	−	0.454707i	$-0.150256\pi$
$401$	413.811	+	716.742i	0.0515330	+	0.0892578i	−0.839108	+	0.543965i	$0.816923\pi$
$402$		0			0
$403$	−3255.85	+	5639.30i	−0.402445	+	0.697056i
$404$	−11256.4			−1.38621
$405$		0			0
$406$	−6504.11			−0.795058
$407$	−5741.36	+	9944.33i	−0.699235	+	1.21111i
$408$		0			0
$409$	4183.82	+	7246.59i	0.505811	+	0.876090i	0.999977	+	0.00672263i	$0.00213989\pi$
$409$	4183.82	+	7246.59i	0.505811	+	0.876090i	−0.494167	+	0.869367i	$0.664527\pi$
$410$	−1678.50	−	2907.25i	−0.202184	−	0.350192i
$411$		0			0
$412$	−2687.41	+	4654.73i	−0.321357	+	0.556607i
$413$	13103.2			1.56117
$414$		0			0
$415$	988.693			0.116947
$416$	7991.34	−	13841.4i	0.941845	−	1.63132i
$417$		0			0
$418$	6539.87	+	11327.4i	0.765252	+	1.32546i
$419$	2100.36	+	3637.93i	0.244891	+	0.424163i	0.962101	−	0.272694i	$-0.0879145\pi$
$419$	2100.36	+	3637.93i	0.244891	+	0.424163i	−0.717210	+	0.696857i	$0.754581\pi$
$420$		0			0
$421$	−3469.38	+	6009.14i	−0.401632	+	0.695648i	−0.993923	−	0.110077i	$-0.964890\pi$
$421$	−3469.38	+	6009.14i	−0.401632	+	0.695648i	0.592291	+	0.805724i	$0.298224\pi$
$422$	10665.3			1.23028
$423$		0			0
$424$	−242.184			−0.0277394
$425$	−82.3737	+	142.675i	−0.00940168	+	0.0162842i
$426$		0			0
$427$	−13083.8	−	22661.8i	−1.48283	−	2.56835i
$428$	2494.50	+	4320.60i	0.281720	+	0.487953i
$429$		0			0
$430$	3599.22	−	6234.03i	0.403651	−	0.699144i
$431$	−6827.09			−0.762991			−0.381496	−	0.924371i	$-0.624591\pi$
$431$	−6827.09			−0.762991			−0.381496	+	0.924371i	$0.624591\pi$
$432$		0			0
$433$	−2199.59			−0.244124			−0.122062	−	0.992522i	$-0.538951\pi$
$433$	−2199.59			−0.244124			−0.122062	+	0.992522i	$0.538951\pi$
$434$	−6752.39	+	11695.5i	−0.746832	+	1.29355i
$435$		0			0
$436$	1786.78	+	3094.80i	0.196265	+	0.339940i
$437$	−2350.46	−	4071.12i	−0.257295	−	0.445648i
$438$		0			0
$439$	−4162.16	+	7209.07i	−0.452504	+	0.783759i	−0.998541	−	0.0540018i	$-0.982802\pi$
$439$	−4162.16	+	7209.07i	−0.452504	+	0.783759i	0.546037	+	0.837761i	$0.316136\pi$
$440$	−1876.37			−0.203301
$441$		0			0
$442$	1775.45			0.191063
$443$	−5433.41	+	9410.93i	−0.582729	+	1.00932i	0.412426	+	0.910991i	$0.364682\pi$
$443$	−5433.41	+	9410.93i	−0.582729	+	1.00932i	−0.995154	+	0.0983247i	$0.968652\pi$
$444$		0			0
$445$	3411.36	+	5908.65i	0.363402	+	0.629431i
$446$	−3994.41	−	6918.51i	−0.424082	−	0.734532i
$447$		0			0
$448$	11402.6	−	19749.9i	1.20250	−	2.08280i
$449$	4947.73			0.520040			0.260020	−	0.965603i	$-0.416271\pi$
$449$	4947.73			0.520040			0.260020	+	0.965603i	$0.416271\pi$
$450$		0			0
$451$	−6414.18			−0.669694
$452$	8955.69	−	15511.7i	0.931947	−	1.61418i
$453$		0			0
$454$	10822.2	+	18744.7i	1.11875	+	1.93773i
$455$	−4862.07	−	8421.35i	−0.500961	−	0.867690i
$456$		0			0
$457$	7098.85	−	12295.6i	0.726630	−	1.25856i	−0.231669	−	0.972795i	$-0.574419\pi$
$457$	7098.85	−	12295.6i	0.726630	−	1.25856i	0.958299	−	0.285766i	$-0.0922480\pi$
$458$	3690.13			0.376481
$459$		0			0
$460$	3168.89			0.321196
$461$	−9114.02	+	15785.9i	−0.920786	+	1.59485i	−0.122584	+	0.992458i	$0.539118\pi$
$461$	−9114.02	+	15785.9i	−0.920786	+	1.59485i	−0.798202	+	0.602390i	$0.794215\pi$
$462$		0			0
$463$	−2170.59	−	3759.58i	−0.217875	−	0.377370i	0.736283	−	0.676674i	$-0.236579\pi$
$463$	−2170.59	−	3759.58i	−0.217875	−	0.377370i	−0.954158	+	0.299303i	$0.903246\pi$
$464$	−1042.28	−	1805.29i	−0.104282	−	0.180621i
$465$		0			0
$466$	2433.69	−	4215.28i	0.241928	−	0.419032i
$467$	−4919.63			−0.487481			−0.243740	−	0.969841i	$-0.578374\pi$
$467$	−4919.63			−0.487481			−0.243740	+	0.969841i	$0.578374\pi$
$468$		0			0
$469$	2962.80			0.291704
$470$	474.291	−	821.497i	0.0465477	−	0.0806230i
$471$		0			0
$472$	−1962.92	−	3399.88i	−0.191421	−	0.331551i
$473$	−6876.98	−	11911.3i	−0.668508	−	1.15789i
$474$		0			0
$475$	−942.254	+	1632.03i	−0.0910180	+	0.157648i
$476$	2060.31			0.198391
$477$		0			0
$478$	13421.9			1.28432
$479$	2286.41	−	3960.19i	0.218098	−	0.377757i	−0.736128	−	0.676842i	$-0.763348\pi$
$479$	2286.41	−	3960.19i	0.218098	−	0.377757i	0.954226	+	0.299085i	$0.0966814\pi$
$480$		0			0
$481$	8914.64	+	15440.6i	0.845057	+	1.46368i
$482$	−9598.31	−	16624.8i	−0.907035	−	1.57103i
$483$		0			0
$484$	−1659.99	+	2875.19i	−0.155897	+	0.270021i
$485$	−7155.79			−0.669954
$486$		0			0
$487$	15751.5			1.46564			0.732822	−	0.680421i	$-0.238203\pi$
$487$	15751.5			1.46564			0.732822	+	0.680421i	$0.238203\pi$
$488$	−3920.04	+	6789.72i	−0.363631	+	0.629828i
$489$		0			0
$490$	−6429.10	−	11135.5i	−0.592729	−	1.02664i
$491$	7654.18	+	13257.4i	0.703520	+	1.21853i	0.967223	+	0.253928i	$0.0817227\pi$
$491$	7654.18	+	13257.4i	0.703520	+	1.21853i	−0.263703	+	0.964604i	$0.584944\pi$
$492$		0			0
$493$	163.457	−	283.116i	0.0149325	−	0.0258639i
$494$	20309.0			1.84968
$495$		0			0
$496$	−4328.28			−0.391826
$497$	14646.2	−	25367.9i	1.32187	−	2.28955i
$498$		0			0
$499$	−8866.05	−	15356.5i	−0.795389	−	1.37765i	−0.922592	−	0.385777i	$-0.873933\pi$
$499$	−8866.05	−	15356.5i	−0.795389	−	1.37765i	0.127203	−	0.991877i	$-0.459400\pi$
$500$	−635.172	−	1100.15i	−0.0568115	−	0.0984005i
$501$		0			0
$502$	1889.80	−	3273.23i	0.168020	−	0.291019i
$503$	10511.5			0.931775			0.465887	−	0.884844i	$-0.345735\pi$
$503$	10511.5			0.931775			0.465887	+	0.884844i	$0.345735\pi$
$504$		0			0
$505$	−5538.08			−0.488003
$506$	5410.49	−	9371.25i	0.475347	−	0.823326i
$507$		0			0
$508$	7653.18	+	13255.7i	0.668416	+	1.15773i
$509$	9815.42	+	17000.8i	0.854737	+	1.48045i	0.876889	+	0.480693i	$0.159615\pi$
$509$	9815.42	+	17000.8i	0.854737	+	1.48045i	−0.0221524	+	0.999755i	$0.507052\pi$
$510$		0			0
$511$	782.262	−	1354.92i	0.0677206	−	0.117296i
$512$	13722.1			1.18444
$513$		0			0
$514$	−9640.30			−0.827267
$515$	−1322.19	+	2290.09i	−0.113131	+	0.195949i
$516$		0			0
$517$	−906.223	−	1569.62i	−0.0770902	−	0.133524i
$518$	18488.3	+	32022.7i	1.56820	+	2.71621i
$519$		0			0
$520$	−1456.73	+	2523.12i	−0.122849	+	0.212781i
$521$	−88.4336			−0.00743636			−0.00371818	−	0.999993i	$-0.501184\pi$
$521$	−88.4336			−0.00743636			−0.00371818	+	0.999993i	$0.501184\pi$
$522$		0			0
$523$	21346.4			1.78473			0.892363	−	0.451317i	$-0.149046\pi$
$523$	21346.4			1.78473			0.892363	+	0.451317i	$0.149046\pi$
$524$	6479.39	−	11222.6i	0.540178	−	0.935616i
$525$		0			0
$526$	15514.2	+	26871.4i	1.28603	+	2.22747i
$527$	−339.394	−	587.847i	−0.0280535	−	0.0485902i
$528$		0			0
$529$	4138.94	−	7168.86i	0.340178	−	0.589205i
$530$	−559.896			−0.0458874
$531$		0			0
$532$	23567.4			1.92063
$533$	−4979.67	+	8625.03i	−0.404678	+	0.700923i
$534$		0			0
$535$	1227.27	+	2125.70i	0.0991770	+	0.171780i
$536$	−443.842	−	768.757i	−0.0357669	−	0.0619501i
$537$		0			0
$538$	−227.538	+	394.108i	−0.0182340	+	0.0315821i
$539$	−24568.0			−1.96330
$540$		0			0
$541$	−14432.6			−1.14696			−0.573480	−	0.819220i	$-0.694407\pi$
$541$	−14432.6			−1.14696			−0.573480	+	0.819220i	$0.694407\pi$
$542$	−12591.1	+	21808.4i	−0.997850	+	1.72833i
$543$		0			0
$544$	833.027	+	1442.84i	0.0656539	+	0.113716i
$545$	879.084	+	1522.62i	0.0690933	+	0.119673i
$546$		0			0
$547$	8284.80	−	14349.7i	0.647592	−	1.12166i	−0.336105	−	0.941825i	$-0.609110\pi$
$547$	8284.80	−	14349.7i	0.647592	−	1.12166i	0.983696	−	0.179837i	$-0.0575571\pi$
$548$	−14628.5			−1.14033
$549$		0			0
$550$	−4337.92			−0.336308
$551$	1869.75	−	3238.50i	0.144562	−	0.250389i
$552$		0			0
$553$	3034.54	+	5255.98i	0.233349	+	0.404172i
$554$	−7010.80	−	12143.1i	−0.537654	−	0.931245i
$555$		0			0
$556$	12904.1	−	22350.6i	0.984277	−	1.70482i
$557$	−11597.0			−0.882191			−0.441096	−	0.897460i	$-0.645410\pi$
$557$	−11597.0			−0.882191			−0.441096	+	0.897460i	$0.645410\pi$
$558$		0			0
$559$	−21355.9			−1.61584
$560$	3231.79	−	5597.62i	0.243871	−	0.422397i
$561$		0			0
$562$	723.912	+	1253.85i	0.0543352	+	0.0941113i
$563$	−11524.6	−	19961.3i	−0.862709	−	1.49426i	−0.869304	−	0.494278i	$-0.835432\pi$
$563$	−11524.6	−	19961.3i	−0.862709	−	1.49426i	0.00659429	−	0.999978i	$-0.497901\pi$
$564$		0			0
$565$	4406.13	−	7631.64i	0.328084	−	0.568258i
$566$	11079.2			0.822778
$567$		0			0
$568$	−8776.27			−0.648317
$569$	7366.96	−	12759.9i	0.542775	−	0.940114i	−0.455968	−	0.889996i	$-0.650707\pi$
$569$	7366.96	−	12759.9i	0.542775	−	0.940114i	0.998743	−	0.0501179i	$-0.0159597\pi$
$570$		0			0
$571$	−7555.94	−	13087.3i	−0.553776	−	0.959169i	−0.997998	−	0.0632515i	$-0.979853\pi$
$571$	−7555.94	−	13087.3i	−0.553776	−	0.959169i	0.444221	−	0.895917i	$-0.353480\pi$
$572$	13078.9	+	22653.3i	0.956043	+	1.65591i
$573$		0			0
$574$	−10327.5	+	17887.7i	−0.750975	+	1.30073i
$575$	1559.07			0.113074
$576$		0			0
$577$	−26150.5			−1.88676			−0.943380	−	0.331715i	$-0.892373\pi$
$577$	−26150.5			−1.88676			−0.943380	+	0.331715i	$0.892373\pi$
$578$	10376.5	−	17972.7i	0.746724	−	1.29336i
$579$		0			0
$580$	1260.39	+	2183.07i	0.0902328	+	0.156288i
$581$	−3041.61	−	5268.22i	−0.217190	−	0.376184i
$582$		0			0
$583$	−534.894	+	926.463i	−0.0379983	+	0.0658150i
$584$	−468.747			−0.0332139
$585$		0			0
$586$	−758.961			−0.0535023
$587$	1045.77	−	1811.33i	0.0735326	−	0.127362i	−0.826915	−	0.562327i	$-0.809906\pi$
$587$	1045.77	−	1811.33i	0.0735326	−	0.127362i	0.900447	+	0.434965i	$0.143239\pi$
$588$		0			0
$589$	−3882.24	−	6724.24i	−0.271587	−	0.470403i
$590$	−4538.01	−	7860.06i	−0.316656	−	0.548464i
$591$		0			0
$592$	−5925.50	+	10263.3i	−0.411379	+	0.712530i
$593$	−3260.34			−0.225778			−0.112889	−	0.993608i	$-0.536010\pi$
$593$	−3260.34			−0.225778			−0.112889	+	0.993608i	$0.536010\pi$
$594$		0			0
$595$	1013.66			0.0698417
$596$	476.426	−	825.194i	0.0327436	−	0.0567135i
$597$		0			0
$598$	−8400.90	−	14550.8i	−0.574479	−	0.995026i
$599$	−11499.6	−	19917.9i	−0.784410	−	1.35864i	−0.929351	−	0.369197i	$-0.879633\pi$
$599$	−11499.6	−	19917.9i	−0.784410	−	1.35864i	0.144941	−	0.989440i	$-0.453701\pi$
$600$		0			0
$601$	7146.93	−	12378.9i	0.485074	−	0.840173i	−0.514779	−	0.857323i	$-0.672126\pi$
$601$	7146.93	−	12378.9i	0.485074	−	0.840173i	0.999853	+	0.0171500i	$0.00545928\pi$
$602$	−44290.5			−2.99858
$603$		0			0
$604$	−10855.1			−0.731274
$605$	−816.702	+	1414.57i	−0.0548821	+	0.0950586i
$606$		0			0
$607$	8217.04	+	14232.3i	0.549455	+	0.951685i	0.998312	+	0.0580809i	$0.0184981\pi$
$607$	8217.04	+	14232.3i	0.549455	+	0.951685i	−0.448856	+	0.893604i	$0.648169\pi$
$608$	9528.80	+	16504.4i	0.635598	+	1.10089i
$609$		0			0
$610$	−9062.62	+	15696.9i	−0.601532	+	1.04188i
$611$	−2814.19			−0.186334
$612$		0			0
$613$	3674.45			0.242104			0.121052	−	0.992646i	$-0.461373\pi$
$613$	3674.45			0.242104			0.121052	+	0.992646i	$0.461373\pi$
$614$	−3276.45	+	5674.99i	−0.215353	+	0.373003i
$615$		0			0
$616$	5772.46	+	9998.19i	0.377563	+	0.653958i
$617$	4313.78	+	7471.69i	0.281469	+	0.487519i	0.971747	−	0.236026i	$-0.0758450\pi$
$617$	4313.78	+	7471.69i	0.281469	+	0.487519i	−0.690278	+	0.723544i	$0.742512\pi$
$618$		0			0
$619$	654.905	−	1134.33i	0.0425248	−	0.0736551i	−0.843980	−	0.536375i	$-0.819793\pi$
$619$	654.905	−	1134.33i	0.0425248	−	0.0736551i	0.886504	+	0.462720i	$0.153127\pi$
$620$	5234.03			0.339038
$621$		0			0
$622$	−4028.76			−0.259708
$623$	20989.4	−	36354.7i	1.34979	−	2.33791i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−4230.95	−	7328.23i	−0.270132	−	0.467883i
$627$		0			0
$628$	−923.362	+	1599.31i	−0.0586722	+	0.101623i
$629$	−1858.54			−0.117814
$630$		0			0
$631$	14447.2			0.911463			0.455731	−	0.890117i	$-0.349378\pi$
$631$	14447.2			0.911463			0.455731	+	0.890117i	$0.349378\pi$
$632$	909.179	−	1574.74i	0.0572234	−	0.0991138i
$633$		0			0
$634$	−11044.9	−	19130.3i	−0.691875	−	1.19836i
$635$	3765.31	+	6521.71i	0.235310	+	0.407569i
$636$		0			0
$637$	−19073.4	+	33036.2i	−1.18637	+	2.05485i
$638$	8607.88			0.534152
$639$		0			0
$640$	−5683.43			−0.351027
$641$	−10036.6	+	17383.8i	−0.618440	+	1.07117i	0.371330	+	0.928501i	$0.378902\pi$
$641$	−10036.6	+	17383.8i	−0.618440	+	1.07117i	−0.989770	+	0.142669i	$0.954431\pi$
$642$		0			0
$643$	8867.96	+	15359.8i	0.543885	+	0.942037i	0.998676	+	0.0514386i	$0.0163807\pi$
$643$	8867.96	+	15359.8i	0.543885	+	0.942037i	−0.454791	+	0.890598i	$0.650286\pi$
$644$	−9748.75	−	16885.3i	−0.596513	−	1.03319i
$645$		0			0
$646$	−1058.52	+	1833.40i	−0.0644686	+	0.111663i
$647$	11456.8			0.696158			0.348079	−	0.937465i	$-0.386834\pi$
$647$	11456.8			0.696158			0.348079	+	0.937465i	$0.386834\pi$
$648$		0			0
$649$	−17341.4			−1.04886
$650$	−3367.75	+	5833.12i	−0.203222	+	0.351990i
$651$		0			0
$652$	5605.12	+	9708.36i	0.336677	+	0.583142i
$653$	14536.0	+	25177.0i	0.871113	+	1.50881i	0.860847	+	0.508864i	$0.169935\pi$
$653$	14536.0	+	25177.0i	0.871113	+	1.50881i	0.0102660	+	0.999947i	$0.496732\pi$
$654$		0			0
$655$	3187.81	−	5521.45i	0.190165	−	0.329376i
$656$	−6619.90			−0.393999
$657$		0			0
$658$	−5836.43			−0.345787
$659$	−2177.54	+	3771.62i	−0.128718	+	0.222946i	−0.923180	−	0.384368i	$-0.874419\pi$
$659$	−2177.54	+	3771.62i	−0.128718	+	0.222946i	0.794462	+	0.607314i	$0.207753\pi$
$660$		0			0
$661$	−13647.7	−	23638.5i	−0.803075	−	1.39097i	−0.917583	−	0.397545i	$-0.869862\pi$
$661$	−13647.7	−	23638.5i	−0.803075	−	1.39097i	0.114508	−	0.993422i	$-0.463471\pi$
$662$	4631.19	+	8021.46i	0.271898	+	0.470941i
$663$		0			0
$664$	−911.297	+	1578.41i	−0.0532608	+	0.0922504i
$665$	11595.0			0.676141
$666$		0			0
$667$	−3093.72			−0.179594
$668$	−20537.4	+	35571.8i	−1.18955	+	2.06035i
$669$		0			0
$670$	−1026.10	−	1777.26i	−0.0591669	−	0.102480i
$671$	17315.8	+	29991.9i	0.996230	+	1.72552i
$672$		0			0
$673$	8880.01	−	15380.6i	0.508617	−	0.880951i	−0.491333	−	0.870972i	$-0.663490\pi$
$673$	8880.01	−	15380.6i	0.508617	−	0.880951i	0.999950	−	0.00997909i	$-0.00317650\pi$
$674$	−33456.3			−1.91200
$675$		0			0
$676$	18287.8			1.04050
$677$	968.667	−	1677.78i	0.0549910	−	0.0952472i	−0.837219	−	0.546867i	$-0.815820\pi$
$677$	968.667	−	1677.78i	0.0549910	−	0.0952472i	0.892210	+	0.451620i	$0.149154\pi$
$678$		0			0
$679$	22014.0	+	38129.4i	1.24421	+	2.15504i
$680$	−151.851	−	263.013i	−0.00856355	−	0.0148325i
$681$		0			0
$682$	8936.48	−	15478.4i	0.501753	−	0.869061i
$683$	2125.71			0.119090			0.0595448	−	0.998226i	$-0.481035\pi$
$683$	2125.71			0.119090			0.0595448	+	0.998226i	$0.481035\pi$
$684$		0			0
$685$	−7197.12			−0.401442
$686$	−17071.7	+	29569.0i	−0.950146	+	1.64570i
$687$		0			0
$688$	−7097.55	−	12293.3i	−0.393301	−	0.681218i
$689$	830.532	+	1438.52i	0.0459227	+	0.0795405i
$690$		0			0
$691$	−6913.13	+	11973.9i	−0.380590	+	0.659201i	−0.991147	−	0.132771i	$-0.957612\pi$
$691$	−6913.13	+	11973.9i	−0.380590	+	0.659201i	0.610557	+	0.791973i	$0.290946\pi$
$692$	27924.8			1.53402
$693$		0			0
$694$	39942.4			2.18472
$695$	6348.74	−	10996.3i	0.346506	−	0.600166i
$696$		0			0
$697$	−519.086	−	899.084i	−0.0282092	−	0.0488597i
$698$	2509.98	+	4347.42i	0.136109	+	0.235748i
$699$		0			0
$700$	−3908.08	+	6768.99i	−0.211016	+	0.365491i
$701$	24464.0			1.31810			0.659052	−	0.752097i	$-0.270958\pi$
$701$	24464.0			1.31810			0.659052	+	0.752097i	$0.270958\pi$
$702$		0			0
$703$	−21259.5			−1.14056
$704$	−15090.8	+	26138.0i	−0.807892	+	1.39931i
$705$		0			0
$706$	−15474.8	−	26803.1i	−0.824931	−	1.42882i
$707$	17037.3	+	29509.5i	0.906300	+	1.56976i
$708$		0			0
$709$	14749.1	−	25546.2i	0.781263	−	1.35319i	−0.149944	−	0.988695i	$-0.547909\pi$
$709$	14749.1	−	25546.2i	0.781263	−	1.35319i	0.931206	−	0.364492i	$-0.118757\pi$
$710$	−20289.6			−1.07247
$711$		0			0
$712$	−12577.3			−0.662012
$713$	−3211.81	+	5563.02i	−0.168700	+	0.292198i
$714$		0			0
$715$	6434.72	+	11145.3i	0.336566	+	0.582950i
$716$	−14422.6	−	24980.7i	−0.752790	−	1.30387i
$717$		0			0
$718$	−4133.81	+	7159.98i	−0.214864	+	0.372156i
$719$	3857.66			0.200093			0.100046	−	0.994983i	$-0.468101\pi$
$719$	3857.66			0.200093			0.100046	+	0.994983i	$0.468101\pi$
$720$		0			0
$721$	16270.2			0.840410
$722$	2507.66	−	4343.39i	0.129260	−	0.223884i
$723$		0			0
$724$	−17491.4	−	30295.9i	−0.897874	−	1.55516i
$725$	620.105	+	1074.05i	0.0317657	+	0.0550197i
$726$		0			0
$727$	−4372.55	+	7573.48i	−0.223066	+	0.386361i	−0.955737	−	0.294221i	$-0.904940\pi$
$727$	−4372.55	+	7573.48i	−0.223066	+	0.386361i	0.732672	+	0.680582i	$0.238273\pi$
$728$	17925.8			0.912604
$729$		0			0
$730$	−1083.68			−0.0549436
$731$	1113.08	−	1927.91i	0.0563184	−	0.0975463i
$732$		0			0
$733$	4709.20	+	8156.58i	0.237296	+	0.411010i	0.959938	−	0.280214i	$-0.0904054\pi$
$733$	4709.20	+	8156.58i	0.237296	+	0.411010i	−0.722641	+	0.691223i	$0.757072\pi$
$734$	−13854.9	−	23997.4i	−0.696723	−	1.20676i
$735$		0			0
$736$	7883.26	−	13654.2i	0.394811	−	0.683832i
$737$	−3921.13			−0.195979
$738$		0			0
$739$	6219.42			0.309587			0.154794	−	0.987947i	$-0.450529\pi$
$739$	6219.42			0.309587			0.154794	+	0.987947i	$0.450529\pi$
$740$	7165.49	−	12411.0i	0.355958	−	0.616537i
$741$		0			0
$742$	1722.46	+	2983.39i	0.0852204	+	0.147606i
$743$	−14693.7	−	25450.3i	−0.725518	−	1.25663i	−0.958760	−	0.284216i	$-0.908267\pi$
$743$	−14693.7	−	25450.3i	−0.725518	−	1.25663i	0.233242	−	0.972419i	$-0.425067\pi$
$744$		0			0
$745$	234.398	−	405.989i	0.0115271	−	0.0199655i
$746$	56758.5			2.78563
$747$		0			0
$748$	−2726.72			−0.133287
$749$	7551.15	−	13079.0i	0.368375	−	0.638045i
$750$		0			0
$751$	10823.6	+	18747.0i	0.525909	+	0.910901i	0.999544	+	0.0301801i	$0.00960808\pi$
$751$	10823.6	+	18747.0i	0.525909	+	0.910901i	−0.473636	+	0.880721i	$0.657059\pi$
$752$	−935.287	−	1619.97i	−0.0453543	−	0.0785559i
$753$		0			0
$754$	6682.75	−	11574.9i	0.322774	−	0.559061i
$755$	−5340.65			−0.257438
$756$		0			0
$757$	−13907.2			−0.667722			−0.333861	−	0.942622i	$-0.608352\pi$
$757$	−13907.2			−0.667722			−0.333861	+	0.942622i	$0.608352\pi$
$758$	6815.48	−	11804.8i	0.326582	−	0.565657i
$759$		0			0
$760$	−1736.98	−	3008.55i	−0.0829040	−	0.143594i
$761$	−11953.0	−	20703.3i	−0.569379	−	0.986193i	−0.996628	−	0.0820585i	$-0.973851\pi$
$761$	−11953.0	−	20703.3i	−0.569379	−	0.986193i	0.427249	−	0.904134i	$-0.359483\pi$
$762$		0			0
$763$	5408.82	−	9368.35i	0.256635	−	0.444504i
$764$	7584.42			0.359155
$765$		0			0
$766$	9974.70			0.470497
$767$	−13463.1	+	23318.7i	−0.633798	+	1.09777i
$768$		0			0
$769$	12555.8	+	21747.3i	0.588783	+	1.01980i	0.994392	+	0.105755i	$0.0337261\pi$
$769$	12555.8	+	21747.3i	0.588783	+	1.01980i	−0.405609	+	0.914047i	$0.632941\pi$
$770$	13345.1	+	23114.5i	0.624579	+	1.08180i
$771$		0			0
$772$	−548.319	+	949.716i	−0.0255627	+	0.0442759i
$773$	−14909.4			−0.693729			−0.346865	−	0.937915i	$-0.612754\pi$
$773$	−14909.4			−0.693729			−0.346865	+	0.937915i	$0.612754\pi$
$774$		0			0
$775$	2575.10			0.119355
$776$	6595.62	−	11424.0i	0.305115	−	0.528474i
$777$		0			0
$778$	8506.37	+	14733.5i	0.391990	+	0.678947i
$779$	−5937.70	−	10284.4i	−0.273094	−	0.473013i
$780$		0			0
$781$	−19383.5	+	33573.2i	−0.888087	+	1.53821i
$782$	1751.44			0.0800912
$783$		0			0
$784$	−25356.0			−1.15506
$785$	−454.287	+	786.848i	−0.0206550	+	0.0357756i
$786$		0			0
$787$	1329.38	+	2302.56i	0.0602128	+	0.104292i	0.894560	−	0.446947i	$-0.147489\pi$
$787$	1329.38	+	2302.56i	0.0602128	+	0.104292i	−0.834348	+	0.551239i	$0.814155\pi$
$788$	−17078.6	−	29581.0i	−0.772082	−	1.33728i
$789$		0			0
$790$	2101.90	−	3640.60i	0.0946610	−	0.163958i
$791$	−54220.0			−2.43722
$792$		0			0
$793$	53772.7			2.40798
$794$	10571.1	−	18309.7i	0.472488	−	0.818373i
$795$		0			0
$796$	−6956.33	−	12048.7i	−0.309750	−	0.536502i
$797$	−7086.11	−	12273.5i	−0.314935	−	0.545483i	0.664489	−	0.747298i	$-0.268649\pi$
$797$	−7086.11	−	12273.5i	−0.314935	−	0.545483i	−0.979424	+	0.201815i	$0.935316\pi$
$798$		0			0
$799$	146.677	−	254.053i	0.00649446	−	0.0112487i
$800$	−6320.48			−0.279329
$801$		0			0
$802$	−3527.14			−0.155296
$803$	−1035.29	+	1793.17i	−0.0454975	+	0.0788040i
$804$		0			0
$805$	−4796.31	−	8307.45i	−0.209997	−	0.363726i
$806$	−13875.7	−	24033.4i	−0.606391	−	1.05030i
$807$		0			0
$808$	5104.55	−	8841.34i	0.222249	−	0.384947i
$809$	21077.7			0.916012			0.458006	−	0.888949i	$-0.348564\pi$
$809$	21077.7			0.916012			0.458006	+	0.888949i	$0.348564\pi$
$810$		0			0
$811$	−11937.4			−0.516868			−0.258434	−	0.966029i	$-0.583206\pi$
$811$	−11937.4			−0.516868			−0.258434	+	0.966029i	$0.583206\pi$
$812$	7754.94	−	13431.9i	0.335154	−	0.580503i
$813$		0			0
$814$	−24468.4	−	42380.5i	−1.05358	−	1.82486i
$815$	2757.68	+	4776.44i	0.118524	+	0.205290i
$816$		0			0
$817$	12732.3	−	22052.9i	0.545221	−	0.944350i
$818$	−35661.0			−1.52428
$819$		0			0
$820$	8005.20			0.340919
$821$	7400.25	−	12817.6i	0.314580	−	0.544869i	−0.664768	−	0.747050i	$-0.731470\pi$
$821$	7400.25	−	12817.6i	0.314580	−	0.544869i	0.979348	+	0.202181i	$0.0648029\pi$
$822$		0			0
$823$	−16588.3	−	28731.8i	−0.702591	−	1.21692i	−0.967554	−	0.252665i	$-0.918693\pi$
$823$	−16588.3	−	28731.8i	−0.702591	−	1.21692i	0.264963	−	0.964259i	$-0.414640\pi$
$824$	−2437.37	−	4221.64i	−0.103046	−	0.178480i
$825$		0			0
$826$	−27921.4	+	48361.3i	−1.17616	+	2.03717i
$827$	29001.3			1.21944			0.609718	−	0.792619i	$-0.291283\pi$
$827$	29001.3			1.21944			0.609718	+	0.792619i	$0.291283\pi$
$828$		0			0
$829$	13221.1			0.553904			0.276952	−	0.960884i	$-0.410676\pi$
$829$	13221.1			0.553904			0.276952	+	0.960884i	$0.410676\pi$
$830$	−2106.80	+	3649.08i	−0.0881060	+	0.152604i
$831$		0			0
$832$	23431.6	+	40584.7i	0.976374	+	1.69113i
$833$	−1988.24	−	3443.73i	−0.0826991	−	0.143239i
$834$		0			0
$835$	−10104.3	+	17501.1i	−0.418769	+	0.725329i
$836$	−31190.3			−1.29036
$837$		0			0
$838$	−17902.5			−0.737987
$839$	−21062.0	+	36480.4i	−0.866675	+	1.50112i	−0.00129985	+	0.999999i	$0.500414\pi$
$839$	−21062.0	+	36480.4i	−0.866675	+	1.50112i	−0.865375	+	0.501125i	$0.832920\pi$
$840$		0			0
$841$	10964.0	+	18990.2i	0.449547	+	0.778638i
$842$	−14785.7	−	25609.6i	−0.605166	−	1.04818i
$843$		0			0
$844$	−12716.4	+	22025.4i	−0.518621	+	0.898278i
$845$	8997.45			0.366298
$846$		0			0
$847$	10050.0			0.407700
$848$	−552.049	+	956.177i	−0.0223555	+	0.0387208i
$849$		0			0
$850$	−351.059	−	608.051i	−0.0141661	−	0.0245365i
$851$	8794.07	+	15231.8i	0.354238	+	0.613559i
$852$		0			0
$853$	−7215.84	+	12498.2i	−0.289643	+	0.501677i	−0.973725	−	0.227729i	$-0.926870\pi$
$853$	−7215.84	+	12498.2i	−0.289643	+	0.501677i	0.684081	+	0.729406i	$0.260203\pi$
$854$	111521.			4.46857
$855$		0			0
$856$	−4524.80			−0.180671
$857$	8056.71	−	13954.6i	0.321134	−	0.556220i	−0.659588	−	0.751627i	$-0.729269\pi$
$857$	8056.71	−	13954.6i	0.321134	−	0.556220i	0.980722	+	0.195407i	$0.0626027\pi$
$858$		0			0
$859$	11250.2	+	19485.9i	0.446858	+	0.773982i	0.998180	−	0.0603115i	$-0.0192094\pi$
$859$	11250.2	+	19485.9i	0.446858	+	0.773982i	−0.551321	+	0.834293i	$0.685876\pi$
$860$	8582.80	+	14865.8i	0.340315	+	0.589443i
$861$		0			0
$862$	14547.8	−	25197.5i	0.574825	−	0.995626i
$863$	43396.8			1.71175			0.855877	−	0.517180i	$-0.173018\pi$
$863$	43396.8			1.71175			0.855877	+	0.517180i	$0.173018\pi$
$864$		0			0
$865$	13738.8			0.540038
$866$	4687.09	−	8118.28i	0.183919	−	0.318557i
$867$		0			0
$868$	−16101.9	−	27889.4i	−0.629649	−	1.09058i
$869$	−4016.07	−	6956.04i	−0.156773	−	0.271539i
$870$		0			0
$871$	−3044.18	+	5272.67i	−0.118425	+	0.205118i
$872$	−3241.07			−0.125868
$873$		0			0
$874$	20034.3			0.775366
$875$	−1922.75	+	3330.29i	−0.0742865	+	0.128668i
$876$		0			0
$877$	1232.77	+	2135.21i	0.0474659	+	0.0822133i	0.888782	−	0.458330i	$-0.151552\pi$
$877$	1232.77	+	2135.21i	0.0474659	+	0.0822133i	−0.841316	+	0.540543i	$0.818219\pi$
$878$	−17738.2	−	30723.5i	−0.681817	−	1.18094i
$879$		0			0
$880$	−4277.12	+	7408.18i	−0.163843	+	0.283784i
$881$	−24512.9			−0.937412			−0.468706	−	0.883354i	$-0.655280\pi$
$881$	−24512.9			−0.937412			−0.468706	+	0.883354i	$0.655280\pi$
$882$		0			0
$883$	24236.1			0.923679			0.461840	−	0.886963i	$-0.347190\pi$
$883$	24236.1			0.923679			0.461840	+	0.886963i	$0.347190\pi$
$884$	−2116.90	+	3666.57i	−0.0805418	+	0.139502i
$885$		0			0
$886$	−23156.0	−	40107.3i	−0.878036	−	1.52080i
$887$	12599.3	+	21822.7i	0.476939	+	0.826082i	0.999651	−	0.0264274i	$-0.00841308\pi$
$887$	12599.3	+	21822.7i	0.476939	+	0.826082i	−0.522712	+	0.852509i	$0.675080\pi$
$888$		0			0
$889$	23167.1	−	40126.7i	0.874017	−	1.51384i
$890$	−29076.9			−1.09512
$891$		0			0
$892$	19050.3			0.715081
$893$	1677.81	−	2906.05i	0.0628731	−	0.108899i
$894$		0			0
$895$	−7095.81	−	12290.3i	−0.265013	−	0.459016i
$896$	17484.5	+	30284.0i	0.651914	+	1.12915i
$897$		0			0
$898$	−10543.1	+	18261.1i	−0.391789	+	0.678599i
$899$	−5109.87			−0.189570
$900$		0			0
$901$	−173.151			−0.00640233
$902$	13667.9	−	23673.5i	0.504536	−	0.873882i
$903$		0			0
$904$	8122.42	+	14068.5i	0.298836	+	0.517599i
$905$	−8605.62	−	14905.4i	−0.316089	−	0.547482i
$906$		0			0
$907$	−13304.0	+	23043.3i	−0.487049	+	0.843594i	−0.999889	−	0.0148906i	$-0.995260\pi$
$907$	−13304.0	+	23043.3i	−0.487049	+	0.843594i	0.512840	+	0.858484i	$0.328593\pi$
$908$	−51614.0			−1.88642
$909$		0			0
$910$	41442.1			1.50966
$911$	12416.1	−	21505.2i	0.451550	−	0.782108i	−0.546932	−	0.837177i	$-0.684204\pi$
$911$	12416.1	−	21505.2i	0.451550	−	0.782108i	0.998483	+	0.0550686i	$0.0175378\pi$
$912$		0			0
$913$	4025.43	+	6972.25i	0.145917	+	0.252736i
$914$	30253.7	+	52401.0i	1.09486	+	1.89636i
$915$		0			0
$916$	−4399.79	+	7620.66i	−0.158704	+	0.274884i
$917$	−39227.8			−1.41267
$918$		0			0
$919$	−26107.2			−0.937102			−0.468551	−	0.883436i	$-0.655224\pi$
$919$	−26107.2			−0.937102			−0.468551	+	0.883436i	$0.655224\pi$
$920$	−1437.02	+	2489.00i	−0.0514970	+	0.0891954i
$921$		0			0
$922$	−38841.9	−	67276.2i	−1.38741	−	2.40306i
$923$	30096.9	+	52129.3i	1.07329	+	1.85900i
$924$		0			0
$925$	3525.37	−	6106.11i	0.125312	−	0.217046i
$926$	18501.2			0.656573
$927$		0			0
$928$	12542.0			0.443653
$929$	−11680.8	+	20231.7i	−0.412523	+	0.714511i	−0.995165	−	0.0982184i	$-0.968686\pi$
$929$	−11680.8	+	20231.7i	−0.412523	+	0.714511i	0.582642	+	0.812729i	$0.302019\pi$
$930$		0			0
$931$	−22743.0	−	39392.0i	−0.800613	−	1.38670i
$932$	5803.45	+	10051.9i	0.203968	+	0.353283i
$933$		0			0
$934$	10483.2	−	18157.4i	0.367260	−	0.636112i
$935$	−1341.53			−0.0469226
$936$		0			0
$937$	10548.5			0.367775			0.183888	−	0.982947i	$-0.441132\pi$
$937$	10548.5			0.367775			0.183888	+	0.982947i	$0.441132\pi$
$938$	−6313.40	+	10935.1i	−0.219765	+	0.380644i
$939$		0			0
$940$	1131.01	+	1958.96i	0.0392441	+	0.0679727i
$941$	−3245.07	−	5620.62i	−0.112419	−	0.194715i	0.804326	−	0.594188i	$-0.202527\pi$
$941$	−3245.07	−	5620.62i	−0.112419	−	0.194715i	−0.916745	+	0.399473i	$0.869193\pi$
$942$		0			0
$943$	−4912.32	+	8508.38i	−0.169636	+	0.293819i
$944$	−17897.6			−0.617074
$945$		0			0
$946$	58616.4			2.01457
$947$	11753.0	−	20356.8i	0.403295	−	0.698528i	−0.590826	−	0.806799i	$-0.701198\pi$
$947$	11753.0	−	20356.8i	0.403295	−	0.698528i	0.994121	+	0.108271i	$0.0345314\pi$
$948$		0			0
$949$	1607.50	+	2784.26i	0.0549858	+	0.0952382i
$950$	−4015.68	−	6955.35i	−0.137143	−	0.237538i
$951$		0			0
$952$	−934.305	+	1618.26i	−0.0318078	+	0.0550927i
$953$	−6740.26			−0.229106			−0.114553	−	0.993417i	$-0.536544\pi$
$953$	−6740.26			−0.229106			−0.114553	+	0.993417i	$0.536544\pi$
$954$		0			0
$955$	3731.48			0.126437
$956$	−16003.1	+	27718.2i	−0.541399	+	0.937731i
$957$		0			0
$958$	9744.19	+	16877.4i	0.328623	+	0.569191i
$959$	22141.2	+	38349.6i	0.745543	+	1.29132i
$960$		0			0
$961$	9590.57	−	16611.4i	0.321928	−	0.557596i
$962$	−75984.4			−2.54661
$963$		0			0
$964$	45776.8			1.52943
$965$	−269.769	+	467.253i	−0.00899913	+	0.0155870i
$966$		0			0
$967$	−8391.27	−	14534.1i	−0.279054	−	0.483336i	0.692096	−	0.721806i	$-0.256688\pi$
$967$	−8391.27	−	14534.1i	−0.279054	−	0.483336i	−0.971150	+	0.238470i	$0.923354\pi$
$968$	−1505.54	−	2607.67i	−0.0499895	−	0.0865844i
$969$		0			0
$970$	15248.2	−	26410.6i	0.504732	−	0.874221i
$971$	46282.7			1.52964			0.764822	−	0.644242i	$-0.222827\pi$
$971$	46282.7			1.52964			0.764822	+	0.644242i	$0.222827\pi$
$972$		0			0
$973$	−78124.9			−2.57407
$974$	−33564.7	+	58135.8i	−1.10419	+	1.91252i
$975$		0			0
$976$	17871.2	+	30953.8i	0.586109	+	1.01517i
$977$	3383.98	+	5861.22i	0.110812	+	0.191931i	0.916098	−	0.400955i	$-0.131322\pi$
$977$	3383.98	+	5861.22i	0.110812	+	0.191931i	−0.805286	+	0.592886i	$0.797988\pi$
$978$		0			0
$979$	−27778.5	+	48113.7i	−0.906848	+	1.57071i
$980$	30662.0			0.999452
$981$		0			0
$982$	−65240.8			−2.12008
$983$	−25037.4	+	43366.1i	−0.812381	+	1.40708i	0.0988128	+	0.995106i	$0.468496\pi$
$983$	−25037.4	+	43366.1i	−0.812381	+	1.40708i	−0.911194	+	0.411979i	$0.864838\pi$
$984$		0			0
$985$	−8402.55	−	14553.6i	−0.271805	−	0.470779i
$986$	696.618	+	1206.58i	0.0224998	+	0.0389708i
$987$		0			0
$988$	−24214.7	+	41941.0i	−0.779728	+	1.35053i
$989$	−21067.0			−0.677343
$990$		0			0
$991$	−2658.60			−0.0852200			−0.0426100	−	0.999092i	$-0.513567\pi$
$991$	−2658.60			−0.0852200			−0.0426100	+	0.999092i	$0.513567\pi$
$992$	13020.7	−	22552.6i	0.416742	−	0.721819i
$993$		0			0
$994$	62418.7	+	108112.i	1.99175	+	3.44981i
$995$	−3422.46	−	5927.88i	−0.109045	−	0.188871i
$996$		0			0
$997$	30310.0	−	52498.5i	0.962817	−	1.66765i	0.247449	−	0.968901i	$-0.420408\pi$
$997$	30310.0	−	52498.5i	0.962817	−	1.66765i	0.715368	−	0.698748i	$-0.246259\pi$
$998$	75570.3			2.39693
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.e.c.46.2		14
3.2	odd	2		45.4.e.c.16.6	✓	14
9.2	odd	6		405.4.a.m.1.2		7
9.4	even	3	inner	135.4.e.c.91.2		14
9.5	odd	6		45.4.e.c.31.6	yes	14
9.7	even	3		405.4.a.n.1.6		7
15.2	even	4		225.4.k.d.124.12		28
15.8	even	4		225.4.k.d.124.3		28
15.14	odd	2		225.4.e.d.151.2		14
45.14	odd	6		225.4.e.d.76.2		14
45.23	even	12		225.4.k.d.49.12		28
45.29	odd	6		2025.4.a.bb.1.6		7
45.32	even	12		225.4.k.d.49.3		28
45.34	even	6		2025.4.a.ba.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.6	✓	14	3.2	odd	2
45.4.e.c.31.6	yes	14	9.5	odd	6
135.4.e.c.46.2		14	1.1	even	1	trivial
135.4.e.c.91.2		14	9.4	even	3	inner
225.4.e.d.76.2		14	45.14	odd	6
225.4.e.d.151.2		14	15.14	odd	2
225.4.k.d.49.3		28	45.32	even	12
225.4.k.d.49.12		28	45.23	even	12
225.4.k.d.124.3		28	15.8	even	4
225.4.k.d.124.12		28	15.2	even	4
405.4.a.m.1.2		7	9.2	odd	6
405.4.a.n.1.6		7	9.7	even	3
2025.4.a.ba.1.2		7	45.34	even	6
2025.4.a.bb.1.6		7	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.13089 + 3.69081i) q^{2} +(-5.08138 - 8.80120i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-15.3820 + 26.6423i) q^{7} +9.21718 q^{8} +O(q^{10})\)	\(q+(-2.13089 + 3.69081i) q^{2} +(-5.08138 - 8.80120i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-15.3820 + 26.6423i) q^{7} +9.21718 q^{8} +21.3089 q^{10} +(20.3573 - 35.2599i) q^{11} +(-31.6089 - 54.7482i) q^{13} +(-65.5545 - 113.544i) q^{14} +(21.0102 - 36.3908i) q^{16} +6.58990 q^{17} +75.3803 q^{19} +(-25.4069 + 44.0060i) q^{20} +(86.7584 + 150.270i) q^{22} +(-31.1814 - 54.0077i) q^{23} +(-12.5000 + 21.6506i) q^{25} +269.420 q^{26} +312.646 q^{28} +(24.8042 - 42.9621i) q^{29} +(-51.5021 - 89.2043i) q^{31} +(126.410 + 218.948i) q^{32} +(-14.0423 + 24.3221i) q^{34} +153.820 q^{35} -282.029 q^{37} +(-160.627 + 278.214i) q^{38} +(-23.0430 - 39.9116i) q^{40} +(-78.7700 - 136.434i) q^{41} +(168.907 - 292.555i) q^{43} -413.773 q^{44} +265.776 q^{46} +(22.2579 - 38.5518i) q^{47} +(-301.710 - 522.577i) q^{49} +(-53.2722 - 92.2702i) q^{50} +(-321.234 + 556.393i) q^{52} -26.2752 q^{53} -203.573 q^{55} +(-141.778 + 245.567i) q^{56} +(105.710 + 183.095i) q^{58} +(-212.963 - 368.863i) q^{59} +(-425.297 + 736.637i) q^{61} +438.981 q^{62} -741.296 q^{64} +(-158.045 + 273.741i) q^{65} +(-48.1538 - 83.4048i) q^{67} +(-33.4858 - 57.9990i) q^{68} +(-327.773 + 567.719i) q^{70} -952.164 q^{71} -50.8558 q^{73} +(600.973 - 1040.92i) q^{74} +(-383.036 - 663.437i) q^{76} +(626.271 + 1084.73i) q^{77} +(98.6395 - 170.849i) q^{79} -210.102 q^{80} +671.400 q^{82} +(-98.8693 + 171.247i) q^{83} +(-16.4747 - 28.5351i) q^{85} +(719.844 + 1246.81i) q^{86} +(187.637 - 324.997i) q^{88} -1364.54 q^{89} +1944.83 q^{91} +(-316.889 + 548.868i) q^{92} +(94.8583 + 164.299i) q^{94} +(-188.451 - 326.406i) q^{95} +(715.579 - 1239.42i) q^{97} +2571.64 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8	\( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8} + 20 q^{10} - 23 q^{11} - 96 q^{13} + 21 q^{14} - 324 q^{16} + 322 q^{17} + 558 q^{19} - 180 q^{20} - 311 q^{22} - 96 q^{23} - 175 q^{25} - 716 q^{26} + 674 q^{28} + 296 q^{29} - 244 q^{31} + 314 q^{32} - 125 q^{34} + 220 q^{35} + 808 q^{37} - 305 q^{38} - 90 q^{40} + 47 q^{41} - 525 q^{43} + 110 q^{44} + 1434 q^{46} - 164 q^{47} - 1225 q^{49} - 50 q^{50} - 1682 q^{52} + 1012 q^{53} + 230 q^{55} + 981 q^{56} - 1183 q^{58} + 85 q^{59} - 828 q^{61} - 1572 q^{62} + 4472 q^{64} - 480 q^{65} - 1093 q^{67} - 2473 q^{68} + 105 q^{70} + 656 q^{71} + 4170 q^{73} + 1316 q^{74} - 2789 q^{76} - 24 q^{77} - 2110 q^{79} + 3240 q^{80} - 124 q^{82} - 1290 q^{83} - 805 q^{85} + 2569 q^{86} - 2271 q^{88} - 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 517 q^{94} - 1395 q^{95} - 1787 q^{97} + 2558 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8 + 20 * q^10 - 23 * q^11 - 96 * q^13 + 21 * q^14 - 324 * q^16 + 322 * q^17 + 558 * q^19 - 180 * q^20 - 311 * q^22 - 96 * q^23 - 175 * q^25 - 716 * q^26 + 674 * q^28 + 296 * q^29 - 244 * q^31 + 314 * q^32 - 125 * q^34 + 220 * q^35 + 808 * q^37 - 305 * q^38 - 90 * q^40 + 47 * q^41 - 525 * q^43 + 110 * q^44 + 1434 * q^46 - 164 * q^47 - 1225 * q^49 - 50 * q^50 - 1682 * q^52 + 1012 * q^53 + 230 * q^55 + 981 * q^56 - 1183 * q^58 + 85 * q^59 - 828 * q^61 - 1572 * q^62 + 4472 * q^64 - 480 * q^65 - 1093 * q^67 - 2473 * q^68 + 105 * q^70 + 656 * q^71 + 4170 * q^73 + 1316 * q^74 - 2789 * q^76 - 24 * q^77 - 2110 * q^79 + 3240 * q^80 - 124 * q^82 - 1290 * q^83 - 805 * q^85 + 2569 * q^86 - 2271 * q^88 - 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 517 * q^94 - 1395 * q^95 - 1787 * q^97 + 2558 * q^98

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